Are there any known formulas or other ways to create a realistic physics animation?
[I am not an animator, and this opinion is solely based on conversations with animators and reading various articles on the subject]

Some things can be simulated to add realism, and blender supports several types of simulations: fluid, newtonian (bullet) physics, smoke and cloth and hair.
You can theoretically use the bullet physics engine to simulate what happens after a fist hits an obstacle.

You can also use motion capture (mocap) to record real motion and use this data in animation.

However, in most VFX and animated films, mocap and simulations aren't usually used just as they are. They're usually the basis or reference for enhanced, exaggerated, stylized or precisely controlled animated sequences.

Cloth, hair, fire/smoke and fluid sims are very useful for producing quick and realistic results in these departments and are more likely to be used as they are (except for some cleaning and fine tuning), especially for background animations. But animators often want more precise control over the end-result than simply running a simulation for main characters' animations.

So the short answer is: yes, you might be able to simulate some things instead of hand-animating them, or to use motion capture to acquire real motion data; but  you might not want to use these exclusively.